Dynamical systems, graphs, and algorithms / George Osipenko.

By:

Osipenko, George

Material type: Text

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783540355953
3540355952
3540355936
9783540355939
1280700300
9781280700309
6610700303
9786610700301

Subject(s): Genre/Form:

Conference papers and proceedings

Additional physical formats: Print version:: Dynamical systems, graphs, and algorithms.DDC classification:

515.39 22

LOC classification:

QA614.85 .O84 2007eb

Other classification:

30.10
31.12
31.65
SI 850
MAT 665f
MAT 055f
MAT 344f
00.04
37
SK 520

Online resources:

Click here to access online

Contents:

Symbolic image -- Periodic trajectories -- Newton's method -- Invariant sets -- Chain recurrent set -- Attractors -- Filtration -- Structural graph -- Entropy -- Projective space and Lyapunov exponents -- Morse spectrum -- Hyperbolicity and structural stability -- Controllability -- Invariant manifolds -- Ikeda mapping dynamics -- A dynamical system of mathematical biology -- [Appendix] A. Double logistic map -- [Appendix] B. Implementation of the symbolic image.

Action note:

digitized 2010 HathiTrust Digital Library committed to preserve

In: Springer e-booksSummary: The modern theory and practice of dynamical systems requires the study of structures that fall outside the scope of traditional subjects of mathematical analysis. An important tool to investigate such complicated phenomena as chaos and strange attractors is the method of symbolic dynamics. This book describes a family of the algorithms to study global structure of systems. By a finite covering of the phase space we construct a directed graph (symbolic image) with vertices corresponding to cells of the covering and edges corresponding to admissible transitions. The method is used to localize the periodic orbits and the chain recurrent set, to construct the attractors and their basins, to estimate the entropy, Lyapunov exponents and the Morse spectrum, to verify the hyperbolicity and the structural stability. Considerable information can be obtained thus, and more techniques may be discovered in future research.

Holdings ( 1 )
Title notes ( 10 )

Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
eBook	e-Library	eBook LN Mathematic		Available

Total holds: 0

Includes bibliographical references and index.

The modern theory and practice of dynamical systems requires the study of structures that fall outside the scope of traditional subjects of mathematical analysis. An important tool to investigate such complicated phenomena as chaos and strange attractors is the method of symbolic dynamics. This book describes a family of the algorithms to study global structure of systems. By a finite covering of the phase space we construct a directed graph (symbolic image) with vertices corresponding to cells of the covering and edges corresponding to admissible transitions. The method is used to localize the periodic orbits and the chain recurrent set, to construct the attractors and their basins, to estimate the entropy, Lyapunov exponents and the Morse spectrum, to verify the hyperbolicity and the structural stability. Considerable information can be obtained thus, and more techniques may be discovered in future research.

Print version record.

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Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2010. MiAaHDL

Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. MiAaHDL

http://purl.oclc.org/DLF/benchrepro0212

digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL

English.